Systems of ordinary differential equations

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Problem: Find the general solution of the linear system: \[ \left\{\begin{array}{l} \dot{x}=2 x+y \\ \dot{y}=4 x-y \end{array} .\right. \]

8.3.16 Systems of ordinary differential equations

1.21 $

Problem: Find the general solution of the linear system: \[ \left\{\begin{array}{c} \dot{x}=x+2 y \\ \dot{y}=3 x+6 y \end{array} .\right. \]

8.3.17 Systems of ordinary differential equations

1.21 $

Problem: Find the general integral of the non-linear system: \[ \frac{d x}{z^{2}-y^{2}}=\frac{d y}{z}=\frac{d z}{-y} . \]

8.3.18 Systems of ordinary differential equations

2.42 $

Problem: Solve the system of differential equations by bringing it to a second order differential equation: \[ \left\{\begin{array}{l} \frac{d x}{d t}=x+2 y+e^{\prime} \\ \frac{d y}{d t}=2 x+y \end{array} .\right. \]

8.3.19 Systems of ordinary differential equations

2.42 $

Problem: Solve the system of linear differential equations: \[ \frac{d y}{d x}=-\frac{y}{z}+x z, \quad \frac{d z}{d x}=-\frac{2 y}{x^{3}}+\frac{z}{x} . \]

8.3.20 Systems of ordinary differential equations

2.9 $

Problem: Solve the system of linear differential equations: \[ x \frac{d y}{d x}=-y+z x, \quad x^{2} \frac{d z}{d x}=-2 y+z x . \]

8.3.21 Systems of ordinary differential equations

2.42 $

Problem: Solve the system of linear differential equations: \[ x^{\prime}=-\frac{y}{t}, \quad y^{\prime}=-\frac{x}{t} . \]

8.3.22 Systems of ordinary differential equations

1.93 $

Problem: Solve the system of linear differential equations: \[ x^{\prime}=-\frac{2}{t} x, \quad y^{\prime}=y+\frac{t+2}{t} x . \]

8.3.23 Systems of ordinary differential equations

2.9 $

Problem: Find the solution of the system of equations: \[ x^{\prime \prime}=2 x+3 y, y^{\prime \prime}=4 x-2 y \text {. } \]

8.3.24 Systems of ordinary differential equations

1.93 $

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